Stability and Bifurcation of Two Kinds of Three-Dimensional Fractional Lotka-Volterra Systems | Zendy

Jinglei Tian | Zendy; Yongguang Yu | Zendy; Wang Hu | Zendy

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Stability and Bifurcation of Two Kinds of Three-Dimensional Fractional Lotka-Volterra Systems

Author(s) -

Jinglei Tian,

Yongguang Yu,

Wang Hu

Publication year - 2014

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2014/695871

Subject(s) - mathematics , bifurcation , hopf bifurcation , stability (learning theory) , transcritical bifurcation , fractional calculus , order (exchange) , bifurcation diagram , saddle node bifurcation , mathematical analysis , control theory (sociology) , nonlinear system , computer science , physics , control (management) , finance , quantum mechanics , machine learning , artificial intelligence , economics

Two kinds of three-dimensional fractional Lotka-Volterra systems are discussed. For one system, the asymptotic stability of the equilibria is analyzed by providing some sufficient conditions. And bifurcation property is investigated by choosing the fractional order as the bifurcation parameter for the other system. In particular, the critical value of the fractional order is identified at which the Hopf bifurcation may occur. Furthermore, the numerical results are presented to verify the theoretical analysis

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